TL;DR: Feel free to praise your children in front of each other.
There is a lot of popular literature out there dealing with this issue. This answer is more roundabout because it relies to some degree on studies, which don't often address exactly the issue that is of concern to you.
Almost 80% of children grow up with at least one brother or sister. Even though they may not get along all the time, siblings play very positive roles in each other’s lives. Brothers and sisters learn their first lessons about many things, like sharing and getting along with others from one another. They also learn parental values from observation of interactions between their parents and siblings.
Praise is an important part of learning what is and isn't appropriate and desired behavior. In the American Academy of Pediatricians' Bright Futures program, reminding a parent about the value of praise is a prominent theme.
Some parents feel it is important to treat each child the same way. They don't want one child to think they love the other more. Treating your children differently doesn't have to mean you are playing favorites. Each child is an individual, and you should treat him that way. That's part of what makes each child a unique person. It is a way of showing that you appreciate how special each child is.
Praise has most often been studied as a motivator for students. it's shocking that in some school settings, comments about what a student had done incorrectly were 15 times more frequent than comments about what had been done well.
Provided that praise is perceived as sincere, it is particularly beneficial to motivation when it encourages performance attributions to controllable causes, promotes autonomy, enhances competence without an over-reliance on social comparisons, and conveys attainable standards and expectations.
In other words, praising children for things they are able to control (like effort: "You tried hard and did well.") rather than an uncontrollable factor (like intelligence: "You did well. You're smart.") had a much greater beneficial effect on children (many studies show that praising a child's intelligence fosters fear rather than ability.)
Regarding whether to do so in front of the other children, studies have shown that modeling good behavior is important. In school settings, children hearing a child getting praise improve their behavior (vicarious praise). However, for this to be a lasting effect, the observer must also receive intermittent praise. (This effect has been borne out in multiple studies.) Other studies show that older siblings are often important role models for younger children (one common outcome that is measurable is academic success. The younger sibling is more likely to be academically successful if the older sibling is; the converse is also true, but less well understood.)
Pulling a child aside each time to praise them can be onerous, and robs the observing child of reinforcement of your values, so do praise your children in front of each other, but try to praise each child (if it can be done sincerely) for their efforts and achievements.
Avoid comparing your children in front of them, and if one child gets praise from a stranger, it's not unreasonable be proud of that child, but if no one praises the siblings, you can correct that by mentioning their accomplishments and how proud you are of them as well.
How Not to Talk to Your Kids
Vicarious reinforcement: Expected and unexpected effects
Sibling Relationship Predictors of Academic Achievement in Adolescents
