Well as the name says. Both are very popular plugins. Broken Link Remover removes access to the pages. Link juice 301 redirects them to another page. Of course both will conflict. Currently, I have both enabled. What to go with ?
If there are BL's to the pages and you must remove them, you should always 301 redirect them or you will lose the BL's. I've never used either, but it sounds like Link Juice 301 is more appropriate. Or just try experimenting, if they are conflicting anyway, just disable one of them and see if there is any improvement.