On desktop- I would not suggest either- on Laptop here are my thoughts:
I would say that in my experience I have had 3 HPs and 4 Lenovos. All of these computers are still in working order. IMHO:
Main advantage of Lenovo in low price bracket= superior keyboard to pretty much anything in low budget range. 13-15 inch models in their low price range selections however tend to suffer from inconsistent build quality. I would suggest Ideapad s205 with a E-450 processor (assuming you are looking for a portable small laptop).
Main advantage of Lenovo in mid-high bracket= Superior build & unorthodox designs. Swirly screen anybody?. However - safe to say these are outside of your budget.
Main advantage of HP= decent all round, but will develop more flaws from bloat-ware if not deleted. Also tends to be a shoddy long term investment.
I have generally been happy with my HP laptop I have had just under 2 years. However there was a mainboard problem when I first got it and it took HP more than 30 days to diagnose the problem, so they repaired my laptop instead of replacing it with a new one. Just recently the hard drive failed and they sent me a replacement, which I installed. I purchased directly from the HP store, which provided me with the longer 2 year warranty. I am getting ready to help my wife select a new laptop and given my experience I would select a Lenovo over a HP laptop.