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It depends on why they like him.
A Loveable Rogue is a villain that his opposition (and the audience) can root for because they're charismatic and have admirable qualities. Whereas a Villain with Good Publicity may be the exact opposite, but they have a good PR team whose job is to gloss over the villain's negative qualities to make them look good to the public.
Or, it could simply be that their opposition considers them a Worthy Opponent. For example, James Moriarty held Sherlock Holmes in high esteem, because Holmes was among the few who possessed a level of intellect that rivalled his own. The same can be said of Lupin III and Inspector Zenigata.
Edited by MiinU I wouldn't mind failure so much, if I didn't fail so much.
There's also Friendly Enemy, where they're still kind despite being on opposite sides.
Current Project: Incorruptible Pure Pureness
A character is so charismatic that they get support from people the opposing faction.