Yes, the company name can have an effect. I worked early on for a major bank (global name), which made other banks more likely to look at and hire me, which made it even more likely major banks would want me, so I worked for lots of them. Got a bit typecast (but, that's where the money was ...).
So after Dell, you'd perhaps give off more of an "enterprise" vibe (and likely have very dull work!).
With the other company, it sounds like you'd be able to show more practical experience, and a less staid choice of company, which could make you more interesting to younger companies.