This is difficult to say, anonymous, because they both have fantastically similar dispositions. Both are extremely loyal, friendly, and easy to train, both require exactly the same kind of care, and both have excellent hearing and senses of smell, among other physical attributes.
As a traveling companion, it really depends on which region you’re starting in. For many regions, beginning with a fire-type is a bit more challenging than beginning with a rock-type. Additionally, in some regions, the fire stones growlithe need to evolve are rare to nonexistent, which only adds to the challenge. On the other hand, just because rockruff may pose less of a challenge when it comes to the gym circuit and evolution doesn’t necessarily mean it won’t be difficult to handle overall. While it’s true that lycanroc are generally more powerful than arcanine, they’re also generally more fragile as well, and rock-types have more weaknesses than fire-types. Likewise, the midnight form of lycanroc are notoriously rowdier but also slower than either its midday counterpart or arcanine.
As a service pokémon, it’s roughly even … but there’s a footnote to this. Growlithe is slightly easier to train than rockruff when it comes to getting them to heel and work, but rockruff have the ability to sense when their trainers are in need of emotional support, which makes rockruff slightly better as an emotional support pokémon than growlithe. However, growlithe are highly difficult to evolve, so they rarely need retraining because they’ll often remain growlithe for their entire lives. Rockruff, on the other hand, evolve by field experience, which means they can evolve at any time if they’re not wearing specialized collars equipped with everstones. This is dangerous because both of its evolutionary forms may pose a risk to their human partners. Obviously, midnight lycanroc are naturally hot-blooded and must be retrained to heel. Otherwise, they have a tendency to run off and challenge practically any pokémon that wanders into their line of sight. Midday lycanroc, meanwhile, are highly obedient and loyal and thus don’t actually need retraining … it’s just that their manes contain extremely sharp and long rocks that can damage property or anyone that touches them. If these manes are trimmed and smoothed down, then they’re actually fantastic choices for service pokémon, but it’s very rare to find a lycanroc who will sit through such a procedure.