The SPEC-01 is a bit smaller (has a tad less cpu height and gpu length clearance) and has different drive bay configuration when compared to the SPEC-02 and 03.
The SPEC-02 and SPEC-3 has similar specs (no pun intended) and their only difference is the look of the case.
http://www.corsair.com/en/carbide-series-spec-01-red-led-mid-tower-gaming-case
http://www.corsair.com/en/carbide-series-spec-02-red-led-mid-tower-gaming-case
http://www.corsair.com/en/carbide-series-spec-03-orange-led-mid-tower-gaming-case
The SPEC-02 and SPEC-3 would be cooler since they both come with 2 fans while the SPEC-1 has only 1 fan included.
It is tricky to suggest cases since it's a matter of personal preference.
You might want to take a look at these cases in that price range: Corsair 200r, Corsair 300r, NZXT Source 210 Elite, NZXT Source 220, NZXT H230 (silent case) and Cooler Master HAF 912.