Good question. It depends on the client and what he/she prefers (if money is not an issue). Private training is always better because the client gets the full attention of the trainer, is personal (as the title Personal Training), gets better instruction and attention to detail. Group training has its benefits as well not only because of the pricing, but mostly because some people perform and feel more comfortable in a group setting (as others prefer private training).
I know from the trainer’s perspective it’s better for them to offer group training because they can make more money per session and reach more people with this format. But, not all trainers can provide the best possible training in terms of quality and instruction in a group setting (even though they think they can). So, my answer to your question is yes.