This will depend on what form of public transport, for example, rail or bus. We can make a comparison between bus and when you say other means, I believe you are referring to l your personal car.
With respect to the above, there are the obvious disadvantages, for example, travel time, comfort, convenience, and safety.
Public transport can be inherently slower due to strongly enforced speed limits. The larger size of the vehicles which makes it difficult for to accelerate rapidly and attain high speeds. Furthermore, the frequent boarding and alighting of passengers increase travel time significantly, especially if it traverses a very busy route. Although segregated bus Lanes may make it more efficient during peak periods, overall, it tends to be a slower form of travel.
Public bus may be a little uncomfortable, since it may not have possess the fancy gadgets and entertainment such as our favourite Songs playing, the air conditioner set to the exact temperature we want. The seats may also not be as comfortable as we would like. If the bus is really crowded it may also be somewhat of a discomfort since people constantly brush against you or step on your feet in some cases.
If you're someone who does a lot of shopping, the public bus not be very friendly form of travel since you have to carry all of that luggage from stop to stop till you get home. The bus stations may also be far from wherever your final destination is or the next stop. I'm sure nobody likes to walk for 3km or above under the scorching sun. The bus becomes increasingly inconvenient for trips which are indirect, meaning you have to stop at several different locations. Some of which may not be on the same route or line.
There is also the safety issue particularly if you take the bus during odd hours such as late at night or very early in the morning. You may get attacked by an assailant if your area isn't well lit or protected by security.
There are also many advantages of using the public transport system. There's the economic, social and environmental benefit/advantage. Maintaining a private vehicle is very expensive, particularly when you consider the cost of fuel, repair & maintenance, registration, insurance, parking and fines or tickets who you happen to like breaking rules. Public transport helps you avoid all of the aforementioned costs.
In addition, the public transport is relatively safer than passenger cars, since buses often travel at lower speeds. Research consistenly shows the public transport system as being a safer mode of travel. Accidents are far fewer, so consider that your chances of being involved in accident significantly reduces when you opt for the public transport system. It can also foster social harmony since we can interact with many people as we travel. It is also a good system for those who can't drive due to age, disability or poverty.
It is also a more healthy approach because of the walking and standing associated with it. Both of which are known to reduce stress significantly. You can lose weight, help your cardiovascular system and reduce your chances of having diseases such diabetes, hypertension and variety of heart diseases if the public transport system is used more frequently.
Passenger vehicles account for close to 80% of emissions in some nations. Consider that public buses contain as much as 40x to 50x more passengers than a car or jeep, if we consider the average number of passengers being 1.5 persons. New systems such as straddle buses may even accommodate up to a 1000 people. If you considered, the number of passenger cars on the road reduces tremendously, hence, emissions reduce also. The fewer vehicles on the road from the use of public transport also means congestion reduces. Congestion is known to be a major cause of increased fuel consumption and hence emissions.
I hope this has been of some help.