Antenna books follow either the practical approach (e.g. Carr's Practical Antenna Handbook) or the mathematical approach (e.g. Kraus's Antennas). To be a true antenna expert, one needs to know both. But for those of us who are not equipped to handle the mathematical approach, the practical approach will do just fine, in which case I would recommend Carr's Practical Antenna Book and ARRL's Antenna Book. Here are some differences between the two:
1. Carr is more readable.
2. ARRL is more comprehensive, with 2.5 times the number of words as Carr.
3. ARRL has more photographs and better looking sketches.
3. ARRL has a multi-author approach (with technical checks and balances) as opposed to Carr's one-man approach. Carr contains few bibliographical references, whereas ARRL has tons of references for further reading.
My opinion: Carr is better for the beginner, but ARRL is better for details and as a reference book. Better yet, get both books, since they serve complementary purposes.