Based on what you have provided, I assume you are looking at 17.3" laptops. The HP has an i3-4000m and Intel HD 4600 graphics core. The Dell with an A8-7410 and [strike]Radeon R5 (Bristol Ridge)[/strike] Radeon R5 (Beema / Carrizo-L) graphics core.
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Neither are particularly good for playing game. Click the TinyURL link below that will take you to some game benchmark comparisons between the two graphic cores at Notebookcheck.net. One to thing to be aware of is both integrated graphics core are used in different model AMD APUs and Intel CPUs. For example, Notebookcheck typically benchmarks integrated graphics with Core i5 and Core i7 CPUs. They only tested AMD APU with the Radeon R5 (Bristol Ridge) graphics core; the AMD PRO A8-9600B which is a bit more powerful than the A8-7410. That basically means both of those laptops may have lower game performance compared to the benchmarks.
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/tinyurl.com/ycwxwb3y[/strike]
The Radeon R5 (Beema / Carrizo-L) graphics core is less powerful than the Intel HD 4600. In fact, it is less powerful than the Intel HD 4000 in the older 3rd generation Intel Core i3 / i5 / i7 CPUs. This basically means the Core i3-4000m has better CPU and graphics performance.
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Looking at ebay the HP laptop is not listed, however, it seems the Dell 5755 is selling for about $350 with the "Buy Now" option. Based on that I recommend you consider the following used 17.3" HP laptop with a current 8th generation Core i3-8130u CPU and Intel UHD 620 graphics core for $350. The seller has a very high feedback score of over 46k and an overall 98% positive feedback.
https/www.ebay.com/itm/HP-17-BY0061ST-17-3-Laptop-Intel-Core-i3-8130U-8GB-DDR4-1-TB-5400-RPM-SATA-/273533928172
Click following TinyURL link for some gamebenchmark results from Notebookcheck.net for the Radeon R5 (Beema / Carrizo-L), Intel HD 4600 and Intel UHD 620. Note that benchmarks for the Intel graphics are usually done with laptops that have Core i5 or i7 CPUs, which means benchmark results with Core i3 CPUs could be lower.
https/tinyurl.com/yb4g9qru