Ah, split CDs of two bands I've never heard of before. The bane of my  existence. Anyway, Sweden's Let Me Out play tuneful melodic hardcore in  the vein of early H20. There's plenty of catchy riffs and some decent  mosh parts. I've heard a million bands like Let Me Out and I always find  them enjoyable as the next guy. Actually, I usually enjoy them more  than the next guy does. However, there is really nothing that stands out  in these six tracks. Let Me Out is decent but nothing groundbreaking.  If I were in Sweden, I'd probably be friends with the band. 
First  Cut is also from Sweden. No shit, really, on a split entitled Swedish Hardcore split, doesn't that just beat all?  First Cut sounds like Verse, Another Breath, Champion, etc. You know the  sound. Fast hardcore with yelled vocals. Actually, First Cut plays  really fast, that's nice. It's hard to tell one song from another but  each song has a breakdown and part where we all can sing along too.  Typical but like their split mate, enjoyable. I'd probably listen to  more from each of these bands.