The most significant difference between YACC/Bison and ANTLR is the type of grammars these tools can process. YACC/Bison handle LALR grammars, ANTLR handles LL grammars.
Often, people who have worked with LALR grammars for a long time, will find working with LL grammars more difficult and vice versa. That does not mean that the grammars or tools are inherently more difficult to work with. Which tool you find easier to use will mostly come down to familiarity with the type of grammar.
As far as advantages go, there are aspects where LALR grammars have advantages over LL grammars and there are other aspects where LL grammars have advantages over LALR grammars.
YACC/Bison generate table driven parsers, which means the "processing logic" is contained in the parser program's data, not so much in the parser's code. The pay off is that even a parser for a very complex language has a relatively small code footprint. This was more important in the 1960s and 1970s when hardware was very limited. Table driven parser generators go back to this era and small code footprint was a main requirement back then.
ANTLR generates recursive descent parsers, which means the "processing logic" is contained in the parser's code, as each production rule of the grammar is represented by a function in the parser's code. The pay off is that it is easier to understand what the parser is doing by reading its code. Also, recursive descent parsers are typically faster than table driven ones. However, for very complex languages, the code footprint will be larger. This was a problem in the 1960s and 1970s. Back then, only relatively small languages like Pascal for instance were implemented this way due to hardware limitations.
ANTLR generated parsers are typically in the vicinity of 10.000 lines of code and more. Handwritten recursive descent parsers are often in the same ballpark. Wirth's Oberon compiler is perhaps the most compact one with about 4000 lines of code including code generation, but Oberon is a very compact language with only about 40 production rules.
As somebody has pointed out already, a big plus for ANTLR is the graphical IDE tool, called ANTLRworks. It is a complete grammar and language design laboratory. It visualises your grammar rules as you type them and if it finds any conflicts it will show you graphically what the conflict is and what causes it. It can even automatically refactor and resolve conflicts such as left-recursion. Once you have a conflict free grammar, you can let ANTLRworks parse an input file of your language and build a parse tree and AST for you and show the tree graphically in the IDE. This is a very big advantage because it can save you many hours of work: You will find conceptual errors in your language design before you start coding! I have not found any such tool for LALR grammars, it seems there isn't any such tool.
Even to people who do not wish to generate their parsers but hand code them, ANTLRworks is a great tool for language design/prototyping. Quite possibly the best such tool available. Unfortunately, that doesn't help you if you want to build LALR parsers. Switching from LALR to LL simply to take advantage of ANTLRworks may well be worthwhile, but for some people, switching grammar types can be a very painful experience. In other words: YMMV.