Wanting to upgrade a Motobecane Super Mirage with a more modern freewheel than the worn out Suntour unit on it. Looks like I'm between 2 Shimano freewheels a HG37 or TZ21. Looks like they have a slightly different design with respect to the finish and the way the cogs are locked on. Is one preferred over the other ignoring the tooth count differences between them? Is one a higher spec (eg. Tiagra vs Claris)?

HG37
imgur.com/0j1Eb0d

TZ21
imgur.com/ARbgRSK

I have just started using SunRace freewheels and am very happy with them. Roger

I really prefer the UG twisted tooth freewheels, but for HG tooth style, I think the HG37 (marked 'Singapore') is better quality than the TZ21 (marked 'China'). In fact, if you're looking for a 14-28 HG freewheel, I have a 7 speed HG model in front of me that you can have for the cost of postage.

Typically, the HG-series freewheels are higher grade than the TZ-series.

Note that the first one (with threaded lockring) allows the smallest cog to be positioned optimally, then fixed on the splines, which is to preserve the intent of Hyperglide, having all of the tooth features line up a certain way.
I much prefer Uniglide freewheels for friction shifting, it gives a more confident drive that won't ever self-shift without much audible indication occurring first.
I prefer Hyperglide freewheels for indexed shifting, it transmits power more evenly during shifts and so is quieter and doesn't require one to reduce pedaling effort while shifting.
For riders who don't ride out of the saddle much, either type might seem as good and safe as the other, but you sure don't want any slippage while shifting (UG) or unexpected shifting events (HG) while riding off of the saddle!

What year is the Super Mirage? Most would have had a 5 speed freewheel. That kind of limits your options.

My experiences with SunRace freewheels have been poor. They have all been loose on their bearings, causing them to clank noticeably during pedaling in some gear combinations. After a few hundred miles, they had damaged their own internals enough to begin chirping and squealing.

Their friction shifting feel was nice, though.

They're both basically Tourney-level, although the HG37 is theoretically probably slightly higher-grade.

Personally, I'd get whichever you prefer as far as tooth counts.

Thanks for all the replies! I believe it was built in 76. It indeed currently has a Suntour 5 spd, but have an issue where it jumps from the 14t cog to the 22t cog and skips the 17t, forcing an upshift from 22t to 17t after the fact. I believe it to be from wear as I have tried all manner of derailleur adjustments. The current wheel I’m running is spaced at 126mm, so I believe the 7 speed should fit, might be a bit tight with the lowest tooth count cog.

The silver finish on the HG37 is likely to be corrosion resistant.

As far as tooth profiles and friction shifting, I love HG if using an old style drop parallelogram derailleur, like Nuovo Record. With a long travel from upper pulley to the freewheel sprocket, HG grabs the chain earlier with less need to overshift, allowing the chain to run smooth even if the pulley isn't precisely below the sprocket. The single nicest friction shifting I've ever experience is with a Mavic 801 derailleur and 8 speed HG - there is a quite sprocket to ride in with virtually every shifter position.

I can see how this might not be optimal when using a derailleur who's upper pulley is in close contact with freewheel sprockets across their range, like an index derailleur.

You may have to move one of the small spacers from the NDS to the DS side of the axle if it is too tight.

OK, if you've got a 126 wheel in there, yeah, 7 speed should fit. Perhaps a washer needed as above, but more likely not.

Try the Sunrace. Modern shifting and durable. I've ridden quite a few miles on one. I'd only put one on my Peugeot to get rolling for cheap while my custom bike was getting built. Surprisingly good IME.

You'll need a new chain at the same time.

Wear might be the issue with your shifting, but there could be other problems. Typical symptom of a worn freewheel is that it start to skip teeth in one gear. Usually happens while climbing hard or otherwise feeding it a lot of torque.

...the dreaded "Falsetto Neutral?

Any kind of unexpected slippage while honking out of the saddle can put you on the ground and take out your mates as well, so must be avoided.

As for the OP's freewheel having the chain skip past a gear while shifting to larger cogs, that is a sure-fire symptom of the skipped cog being installed backwards.
Except that I'm not certain that a Suntour 5-speed freewheel's 2nd-position (threaded) cog can be installed backwards, or can it?

It's also a common symptom of a flexible chain and/or wider-ratio freewheel combined with a too-large chain gap, which may or may not be adjustable on the OP's particular rear derailer.

I destroyed the bearings and the sprockets of TZ21 in around 8 months, but I used it every day in all weather conditions – had it on my year-round commuter bike that I use in the snowy and slushy winters. The backside of the freewheel is very exposed and water gets inside easily, so I would recommend you to put a spokeguard behind the freewheel or regularly clean and put some dirt and grit repellants on there if you decide to go for TZ21. Overall, I went through two chains on that freewheel until the teeth were worn down, so the metal is rather soft and prone to rust (started rusting after a week). Can't comment on the other one.

+1. I've used them for over a decade. at least 6 in the fleet, 13-25, 13-28, 13-30, all 7 cog.

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Had good experiences with Sunrace as well.

I was going to say Atom since it is French and vintage. If you are riding it a lot I can't argue with getting something new. The other recommendation is, of course, SunTour.

SunTour Winner 6-speed. Some regular spacing, some 'ultra'. I have been hording them for years... at least two good spares of each: 13-18 'corncobs', 13-21, 13-24, 13-26, and 13-28. I think I even have a 13-30 seven-speed somewhere or another...