LITFL have an excellent summary of this topic.

Also, somewhere else on this site is a brief summary of the routes of enteral nutrition.

Advantages

• Easy to insert
• Least uncomfortable in the awake patient
• The tubes are cheap
• With a basic sump tube, one can aspirate the gastric contents and assess the residual volume, thereby keeping an eye on gastric emptying function

Disadvantages

• Traumatic to the mucosa
• sinusitis
• pressure areas on the nares or upper lip
• requires radiological confirmation of placement
• easily dislodged by a delirious patient
• may increase aspiration risk

Nasogastric route of insertion

Advantages

• Easy to insert
• Least uncomfortable in the awake patient
• The tubes are cheap
• With a basic sump tube, one can aspirate the gastric contents and assess the residual volume, thereby keeping an eye on gastric emptying function

Disadvantages

• Traumatic to the mucosa: the coagulopathic patient will have a deluge of epistaxis.
• In the long term, can cause sinusitis
• In the long term, can cause pressure areas on the nares or upper lip
• It requires radiological confirmation of placement
• It is easily dislodged by a delirious patient
• It may increase aspiration risk because the gastro-oesophageal sphincter is less competent when there is something constantly in it

Orogastric route of insertion

Advantages

• Easy to insert (especially with direct laryngoscopy)
• Fewer pressure are complications with long term use
• Less traumatic to mucosa; its the route of choice for the patient with no platelets.

Disadvantages

• The path of insertion is less direct than with the nasal insertion
• Intolerably uncomfortable for the awake patient
• May cause pressure areas on the lips
• May interfere with oral hygiene care (in the sense that another tube in the mouth is something else to get in the nurses' way)