Wargame with customizable miniature stats?
Quite a few, actually, have had such a &quot;Look at it and rate it&quot; approach.
Early Warhammer games
The first edition of Warhammer 40K (Warhammer 40K: Rogue Trader), and the first several editions of Warhammer Fantasy Battles, were all intended to use any minis, and had extensive minis rating lists by base type, weapon, and profile value.
40KRT vehicles were points-costed by their ratings; the rating system wasn't terribly effective at play balance, but it was workable within reason, and especially for man-sized units.
Ground Zero Games' games
GZG's rules are intended for use with both their lines and others' lines of minis. Better still, you can get them in PDF for free direct from GZG.
Dirtside II is vehicle or squad per mini, platoon scaled, up to battalion level. It includes vehicle design rules that border on being &quot;Look and rate&quot;...
Stargrunt II is tactical, squad level, individual man per mini, infantry combat, but it also can use Dirtside II vehicles.
Full Thrust is space combat, one ship per mini. It can do fleet level play easily.
R Talsorian Games' Mekton
Mekton has always been a combined battle game and RPG, and always had a design system capable of producing a wide range of designs.
Because the design system is actually a design system, you might not always be able to get decent match to a given mini's fluff text.
7th Street Games' Mecha
The system is able to use a variety of minis. The included setting is less flexible, being focused on space aztechs.
Dream Pod 9's whole catalogue
The &quot;rating&quot; system in both Heavy Gear and Jovian Chronicles is intended to take an extant mini or image, and allow you to devise game stats to fit, generating a relatively good point total for balance purposes. Other games in the line use the same ratings, so that means that any of them can be used. Several have both minis and RPG rules, and the minis rules are almost all written for hex-grids but easily adapted to gridless play.
Flashpoint!
Flashpoint! is a wonderful minis wargame, using a mostly 1d20 rolls, printed in landscape mode in the 90's, of skirmish scale combat in a near-future sci-fi setting.  1 Character/vehicle/robot per model, typically individual model maneuver scale, and intended for platoon level and below.
Many elements border between a rating system and a design system, especially robots and vehicles.
Old FASA games
VOR is very similar to early WH40K:RT... except using d10's rather than d6's, and having a less-obviously Traveller/Cthulhu mashup setting. The rating system is very similar to that in 40K:RT.
And onto the less close fit to the question...
Battletech, while having a design system rather than a rating system, has rules for mecha, vehicles, and troops, and multiple games in various scales, so you can use pretty much almost your entire collection somewhere... and it's still in print, from Catalyst.
Renegade Legion is very much the same approach as Battletech, but is a different set of combat mechanics.