Honestly, calling a transmission a 3.44 or a 3.88 is not really saying anything.
When discussing gearing, 1st through 4th is important, the final drive is important, and the tire size is important. Without all the variables being noted, just denoting the final drive is meaningless.
Most transmissions use a stock 1-2 and swap 3rd and 4th and the differential. Much cheaper to build this way, custom 3-4 costs about $800 in gears. A custom 1-2 is more like $1300. Do all 4 custom and you're north of $2500 with synchros, shift hubs, and bearings. Then add the ring and pinion, which can range from $300 to $1500 depending on source. If you really go crazy money-wise, get a LSD or a Torsen geared-type differential.
I'm building(whenever all the parts actually arrive!) a 3.44 final drive with close ratio gearing: 3.44 1st, 1.93 second, 1.30 3rd and 1.0 4th. Tire is 24.2 inches tall.
Note that my 4th is pretty darn close to the stock VW 0.89 4th with the VW 3.88 final drive. The transmission is expensive to build(all 4 gears are custom) but is probably as good as a 4 speed can be.
Before the "Way of the 5" folks chime in, I have a Spyder(mid-engine and swing-axle) so yeah, NO 5 speed! It is what it is, I'm not rebuilding the entire rear end just get another gear. There's no need, I don't use the car for interstate cruising. Just back road and mountain twisty work.